The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  1  2  1  1  1  1  2  1  1  1  1  1  1
 0  2  0  0  0  0  0  0  0  0  0  2  2  2  2  2 2a 2a 2a 2a+2  2 2a 2a  2  2 2a+2  2 2a  0  2 2a+2  2 2a+2  0  0  2 2a+2  0
 0  0  2  0  0  0  0  2  2  2 2a 2a+2 2a+2 2a  2 2a  0 2a  0  2 2a+2  0  2  2  2 2a  2  2  2 2a  2 2a+2  2 2a  2  2  0 2a+2
 0  0  0  2  0  0  2 2a+2 2a+2 2a  0  0  2  2 2a 2a 2a+2 2a+2  0  2 2a+2 2a  2 2a+2 2a+2 2a 2a  0 2a+2 2a+2 2a+2  0 2a  0 2a  0  2  0
 0  0  0  0  2  0 2a+2  0 2a+2  2 2a  2  0 2a+2 2a+2 2a 2a+2  0 2a+2 2a+2  2 2a 2a+2  0 2a+2  0 2a 2a+2 2a  2  2  2 2a+2  0  0  0  0 2a+2
 0  0  0  0  0  2  2  2 2a+2 2a+2 2a+2 2a+2  0  0  2  2  0  2  2  2  2 2a 2a 2a+2  0  0  0 2a+2 2a  2 2a  2 2a  2  2 2a 2a+2  2

generates a code of length 38 over GR(16,4) who´s minimum homogenous weight is 96.

Homogenous weight enumerator: w(x)=1x^0+261x^96+366x^100+444x^104+192x^105+498x^108+1728x^109+501x^112+5184x^113+450x^116+5184x^117+540x^120+426x^124+354x^128+168x^132+72x^136+12x^140+3x^144

The gray image is a code over GF(4) with n=152, k=7 and d=96.
This code was found by Heurico 1.16 in 77.2 seconds.